Dissimilarity measure for ranking data via mixture of copulae

We define a new distance measure for ranking data using a mixture of copula\r\nfunctions. Our distance measure evaluates the dissimilarity of subjects’ ranking preferences to segment them via hierarchical cluster analysis. The proposed distance\r\nmeasure builds upon Spearman grade correlation coefficient on a copula transformation of rank denoting the level of importance assigned by subjects on the\r\nclassification of k objects. These mixtures of copulae enable flexible modeling of\r\nthe different types of dependence structures found in data and the consideration of\r\nvarious circumstances in the classification process. For example, by using mixtures\r\nof copulae with lower and upper tail dependence, we can emphasize the agreement\r\non extreme ranks when they are considered important.